OpenRaiser/Intern-Atlas huggingface dataset:
Graph or Relational Databases: A Speed Comparison for Process Mining Algorithm
Venue: arXiv cs.DB 2016
Year: 2016

Process-Aware Information System (PAIS) are IT systems that manages, supports business processes and generate large event logs from execution of business processes. An event log is represented as a tuple of the form CaseID, TimeStamp, Activity and Actor. Process Mining is an emerging area of research that deals with the study and analysis of business processes based on event logs. Process Mining aims at analyzing event logs and discover business process models, enhance them or check for conformance with an a priori model. The large volume of event logs generated are stored in databases. Relational databases perform well for certain class of applications. However, there are certain class of applications for which relational databases are not able to scale. A number of NoSQL databases have emerged to encounter the challenges of scalability. Discovering social network from event logs is one of the most challenging and important Process Mining task. Similar-Task and Sub-Contract algorithms are some of the most widely used Organizational Mining techniques. Our objective is to investigate which of the databases (Relational or Graph) perform better for Organizational Mining under Process Mining. An intersection of Process Mining and Graph Databases can be accomplished by modelling these Organizational Mining metrics with graph databases. We implement Similar-Task and Sub-Contract algorithms on relational and NoSQL (graph-oriented) databases using only query language constructs. We conduct empirical analysis on a large real world data set to compare the performance of row-oriented database and NoSQL graph-oriented database. We benchmark performance factors like query execution time, CPU usage and disk/memory space usage for NoSQL graph-oriented database against row-oriented database.
An initial performance review of software components for a heterogeneous computing platform
Venue: arXiv cs.SE 2016
Year: 2016

The design of embedded systems is a complex activity that involves a lot of decisions. With high performance demands of present day usage scenarios and software, they often involve energy hungry state-of-the-art computing units. While focusing on power consumption of computing units, the physical properties of software are often ignored. Recently, there has been a growing interest to quantify and model the physical footprint of software (e.g. consumed power, generated heat, execution time, etc.), and a component based approach facilitates methods for describing such properties. Based on these, software architects can make energy-efficient software design solutions. This paper presents power consumption and execution time profiling of a component software that can be allocated on heterogeneous computing units (CPU, GPU, FPGA) of a tracked robot.
Improved Stereo Matching with Constant Highway Networks and Reflective Confidence Learning
Venue: arXiv cs.CV 2016
Year: 2016

We present an improved three-step pipeline for the stereo matching problem and introduce multiple novelties at each stage. We propose a new highway network architecture for computing the matching cost at each possible disparity, based on multilevel weighted residual shortcuts, trained with a hybrid loss that supports multilevel comparison of image patches. A novel post-processing step is then introduced, which employs a second deep convolutional neural network for pooling global information from multiple disparities. This network outputs both the image disparity map, which replaces the conventional "winner takes all" strategy, and a confidence in the prediction. The confidence score is achieved by training the network with a new technique that we call the reflective loss. Lastly, the learned confidence is employed in order to better detect outliers in the refinement step. The proposed pipeline achieves state of the art accuracy on the largest and most competitive stereo benchmarks, and the learned confidence is shown to outperform all existing alternatives.
Perfect Sequences and Arrays over the Unit Quaternions
Venue: arXiv cs.IT 2016
Year: 2016

We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have perfect periodic auto- correlation. Furthermore, the first sequence construction generates odd-perfect sequences of unbounded lengths, with good ZCZ.
Adaptive Real-Time Software Defined MIMO Visible Light Communications using Spatial Multiplexing and Spatial Diversity
Venue: arXiv cs.IT 2016
Year: 2016

In this paper, we experimentally demonstrate a real-time software defined multiple input multiple output (MIMO) visible light communication (VLC) system employing link adaptation of spatial multiplexing and spatial diversity. Real-time MIMO signal processing is implemented by using the Field Programmable Gate Array (FPGA) based Universal Software Radio Peripheral (USRP) devices. Software defined implantation of MIMO VLC can assist in enabling an adaptive and reconfigurable communication system without hardware changes. We measured the error vector magnitude (EVM), bit error rate (BER) and spectral efficiency performance for single carrier M-QAM MIMO VLC using spatial diversity and spatial multiplexing. Results show that spatial diversity MIMO VLC improves error performance at the cost of spectral efficiency that spatial multiplexing should enhance. We propose the adaptive MIMO solution that both modulation schema and MIMO schema are dynamically adapted to the changing channel conditions for enhancing the error performance and spectral efficiency. The average error-free spectral efficiency of adaptive 2x2 MIMO VLC achieved 12 b/s/Hz over 2 meters indoor dynamic transmission.
Interaktion mit 3D-Objekten in Augmented Reality Anwendungen auf mobilen Android Geräten
Venue: arXiv cs.HC 2016
Year: 2016

This bachelor's thesis describes the conception and implementation of an augmented reality application for the Android platform. The intention is to demonstrate some possibilities of interaction within an augmented reality environment on mobile devices. For that purpose, a 3D-model is displayed on the devices' touchscreen using marker-based tracking. This enables the user to translate, rotate or scale the model as he wishes. He can additionally select and highlight preassigned parts of the model to display specific information for that element. To assist developers in modifying the application for changing requirements without re-writing large portions of the source code, the information for each part have been encapsulated into its own data type. After an introduction to augmented reality, its underlying technology and the Android platform, some possible usage scenarios and the resulting functionalities are outlined. Finally, the design as well as the developed implementation are described.
Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization
Venue: arXiv cs.LG 2017
Year: 2017

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor placement, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.
Parallelism and Time in Hierarchical Self-Assembly
Venue: arXiv cs.CC 2017
Year: 2017

We study the role that parallelism plays in time complexity of Winfree's abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the "hierarchical" aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the "seeded" aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang ("Running Time and Program Size for Self-Assembled Squares", STOC 2001) showed how to assemble an n x n square in O(n) time in the seeded aTAM using O(log n / log log n) unique tile types, where both of these parameters are optimal. They asked whether the hierarchical aTAM could allow a tile system to use the ability to form large assemblies in parallel before they attach to break the Omega(n) lower bound for assembly time. We show that there is a tile system with the optimal O(log n / log log n) tile types that assembles an n x n square using O(log^2 n) parallel "stages", which is close to the optimal Omega(log n) stages, forming the final n x n square from four n/2 x n/2 squares, which are themselves recursively formed from n/4 x n/4 squares, etc. However, despite this nearly maximal parallelism, the system requires superlinear time to assemble the square. We extend the definition of *partial order tile systems* studied by Adleman et al. in a natural way to hierarchical assembly and show that no hierarchical partial order tile system can build any shape with diameter N in less than time Omega(N), demonstrating that in this case the hierarchical model affords no speedup whatsoever over the seeded model. We strengthen the Omega(N) time lower bound for deterministic seeded systems of Adleman et al. to nondeterministic seeded systems. Finally, we show that for infinitely many n, a tile system can assemble an n x n' rectangle, with n > n', in time O(n^{4/5} log n), breaking the linear-time lower bound.
Facile Algebraic Representation of a Novel Quaternary Logic
Venue: arXiv cs.AR 2017
Year: 2017

In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean algebra for binary domain; yet it does not lack the benefits of a higher-radix system. It offers seamless integration of the binary logic functions and expressions through a set of transforms and allows any binary logic simplification technique to be applied in quaternary domain. Since physical realization of the operators defined in this logic has recently been reported, it has become very important to have a well-defined algebra that will facilitate the algebraic manipulation of the novel quaternary logic and aid in designing various complex logic circuits. Therefore, based on our earlier works, here we describe the complete algebraic representation of this logic for the first time. The efficacy of the logic has been shown by designing and comparing several common logic circuits with existing designs in both binary and quaternary domain.
Hybrid Approximate Message Passing
Venue: arXiv cs.IT 2017
Year: 2017

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.
Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding
Venue: arXiv cs.IT 2017
Year: 2017

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially-coupled GLDPC codes with BCH component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution (DE).
Approximate Revenue Maximization with Multiple Items
Venue: arXiv cs.GT 2017
Year: 2017

Maximizing the revenue from selling _more than one_ good (or item) to a single buyer is a notoriously difficult problem, in stark contrast to the one-good case. For two goods, we show that simple "one-dimensional" mechanisms, such as selling the goods separately, _guarantee_ at least 73% of the optimal revenue when the valuations of the two goods are independent and identically distributed, and at least $50\%$ when they are independent. For the case of $k>2$ independent goods, we show that selling them separately guarantees at least a $c/\log^2 k$ fraction of the optimal revenue; and, for independent and identically distributed goods, we show that selling them as one bundle guarantees at least a $c/\log k$ fraction of the optimal revenue. Additional results compare the revenues from the two simple mechanisms of selling the goods separately and bundled, identify situations where bundling is optimal, and extend the analysis to multiple buyers.
A Simplified Description of Fuzzy TOPSIS
Venue: arXiv cs.AI 2017
Year: 2017

A simplified description of Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) is presented. We have adapted the TOPSIS description from existing Fuzzy theory literature and distilled the bare minimum concepts required for understanding and applying TOPSIS. An example has been worked out to illustrate the application of TOPSIS for a multi-criteria group decision making scenario.
A Simple and Correct Even-Odd Algorithm for the Point-in-Polygon Problem for Complex Polygons
Venue: arXiv cs.CG 2017
Year: 2017

Determining if a point is in a polygon or not is used by a lot of applications in computer graphics, computer games and geoinformatics. Implementing this check is error-prone since there are many special cases to be considered. This holds true in particular for complex polygons whose edges intersect each other creating holes. In this paper we present a simple even-odd algorithm to solve this problem for complex polygons in linear time and prove its correctness for all possible points and polygons. We furthermore provide examples and implementation notes for this algorithm.
Egalitarian Graph Orientations
Venue: arXiv cs.DM 2017
Year: 2017

Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs directed into it. We discuss how this objective arises in problems resulting from telecommunications. We give optimal, polynomial-time algorithms for: finding an orientation that minimizes the lexicographic order of the indegrees and finding a strongly-connected orientation that minimizes the maximum indegree. We show that minimizing the lexicographic order of the indegrees is NP-hard when the resulting orientation is required to be acyclic.
Polarization of the Renyi Information Dimension with Applications to Compressed Sensing
Venue: arXiv cs.IT 2017
Year: 2017

In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi information dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we prove that the RID of an i.i.d. sequence of mixture random variables polarizes to the extremal values of 0 and 1 (corresponding to discrete and continuous distributions) when transformed by a Hadamard matrix. Further, we prove that the polarization pattern of the RID admits a closed form expression and follows exactly the Binary Erasure Channel (BEC) polarization pattern in the discrete setting. We also extend the results from the single- to the multi-terminal setting, obtaining a Slepian-Wolf counterpart of the RID polarization. We discuss applications of the RID polarization to Compressed Sensing of i.i.d. sources. In particular, we use the RID polarization to construct a family of deterministic $\pm 1$-valued sensing matrices for Compressed Sensing. We run numerical simulations to compare the performance of the resulting matrices with that of random Gaussian and random Hadamard matrices. The results indicate that the proposed matrices afford competitive performances while being explicitly constructed.
Sophistication vs Logical Depth
Venue: arXiv cs.IT 2017
Year: 2017

Sophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string that is shortest within some precision; the second can be defined as the minimal computation time of a program that is shortest within some precision. We show that the Busy Beaver function of the sophistication of a string exceeds its logical depth with logarithmically bigger precision, and that logical depth exceeds the Busy Beaver function of sophistication with logarithmically bigger precision. We also show that this is not true if the precision is only increased by a constant (when the notions are defined with plain Kolmogorov complexity). Finally we show that sophistication is unstable in its precision: constant variations can change its value by a linear term in the length of the string.
Confluence of an extension of Combinatory Logic by Boolean constants
Venue: arXiv cs.LO 2017
Year: 2017

We show confluence of a conditional term rewriting system CL-pc${}^1$, which is an extension of Combinatory Logic by Boolean constants. This solves problem 15 from the RTA list of open problems. The proof has been fully formalised in the Coq proof assistant.
Compact Relaxations for MAP Inference in Pairwise MRFs with Piecewise Linear Priors
Venue: arXiv cs.CV 2017
Year: 2017

Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficult, and therefore approximate inference methods based on a linear programming (LP) relaxation are commonly used in practice. In this work we study how compact linear programs can be constructed for general piecwise linear smoothness priors. The number of unknowns is O(LK) per pairwise clique in terms of the state space size $L$ and the number of linear segments K. This compares to an O(L^2) size complexity of the standard LP relaxation if the piecewise linear structure is ignored. Our compact construction and the standard LP relaxation are equivalent and lead to the same (approximate) label assignment.
Formalization, Mechanization and Automation of Gödel's Proof of God's Existence
Venue: arXiv cs.LO 2017
Year: 2017

Gödel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction proof. A formalization of the axioms, definitions and theorems in the TPTP THF syntax. Automatic verification of the consistency of the axioms and definitions with Nitpick. Automatic demonstration of the theorems with the provers LEO-II and Satallax. A step-by-step formalization using the Coq proof assistant. A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.
Algorithms for group isomorphism via group extensions and cohomology
Venue: arXiv cs.DS 2017
Year: 2017

The isomorphism problem for finite groups of order n (GpI) has long been known to be solvable in $n^{\log n+O(1)}$ time, but only recently were polynomial-time algorithms designed for several interesting group classes. Inspired by recent progress, we revisit the strategy for GpI via the extension theory of groups. The extension theory describes how a normal subgroup N is related to G/N via G, and this naturally leads to a divide-and-conquer strategy that splits GpI into two subproblems: one regarding group actions on other groups, and one regarding group cohomology. When the normal subgroup N is abelian, this strategy is well-known. Our first contribution is to extend this strategy to handle the case when N is not necessarily abelian. This allows us to provide a unified explanation of all recent polynomial-time algorithms for special group classes. Guided by this strategy, to make further progress on GpI, we consider central-radical groups, proposed in Babai et al. (SODA 2011): the class of groups such that G mod its center has no abelian normal subgroups. This class is a natural extension of the group class considered by Babai et al. (ICALP 2012), namely those groups with no abelian normal subgroups. Following the above strategy, we solve GpI in $n^{O(\log \log n)}$ time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups. We also solve GpI in $n^{O(\log\log n)}$ time for groups whose solvable normal subgroups are elementary abelian but not necessarily central. As far as we are aware, this is the first time there have been worst-case guarantees on a $n^{o(\log n)}$-time algorithm that tackles both aspects of GpI---actions and cohomology---simultaneously.
Ultimate Positivity is Decidable for Simple Linear Recurrence Sequences
Venue: arXiv cs.CC 2017
Year: 2017

We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are positive. Using lower bounds in Diophantine approximation concerning sums of S-units, we show that for simple LRS (those whose characteristic polynomial has no repeated roots) the Ultimate Positivity Problem is decidable in polynomial space. If we restrict to simple LRS of a fixed order then we obtain a polynomial-time decision procedure. As a complexity lower bound we show that Ultimate Positivity for simple LRS is hard for co$\exists\mathbb{R}$, i.e., the class of problems solvable in the universal theory of the reals (which lies between coNP and PSPACE).